A New York judge declined to toss out former Fox News executive Laura Luhn’s lawsuit against the network and its then-parent company over the settlement of her claims that ex-network head Roger Ailes abused her and tried to blackmail her.

Luhn is challenging an agreement she signed with the network, claiming that it was entered into under duress. The agreement was for her then salary of $250,000, to be paid annually until her retirement age, which was 12 years from the time it was signed.

The judge, Lyle Frank, rejected the company’s motion to dismiss. He wrote that the complaint “is replete with factual allegations regarding duress and her inability to report the alleged sexual abuse and misconduct while it was occurring. At this stage of the litigation, the duress that is alleged that occurred prior to the negotiation of the agreement between the parties is enough for this case not to be dismissed,...